C1 Introduction to Interactions. Models

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1 C1 Introduction to Interactions Models Scientists create models to explain the world Models compress complex phenomena into bite-sized chunks that we can digest and understand Models simplify and reduce complexity General Physics C1 1 General Physics C1 2 1

Schematic History of Physics Volume C, page 6 Two

Covers gravity Phenomena at distance scales larger

Covers all distance scales Rarely used in practice

2 Schematic History of Physics Volume C, page 6 Two Fundamental Models of Physics General Relativity Covers gravity Phenomena at distance scales larger than atoms Standard Model Does not cover gravity Covers all distance scales Rarely used in practice Exotic cases General Physics C1 3 General Physics C1 4 2

3 Five Simpler Theories Current Conceptual Structure Newtonian Mechanics Special Relativity Electromagnetic Field Theory Quantum Mechanics Statistical Mechanics Each has it s own more limited range of validity Much easier to use within range General Physics C1 5 General Physics C1 6 3

Emmy Noether Noether's theorem States that to every continuous symmetry of a physical theory there corresponds a conserved quantity i.e. a physical quantity that does not change with time Allows us to derive conserved quantities from the mathematical form of our theories.

4 Emmy Noether Noether's theorem States that to every continuous symmetry of a physical theory there corresponds a conserved quantity i.e. a physical quantity that does not change with time Allows us to derive conserved quantities from the mathematical form of our theories. General Physics C1 7 Symmetry Symmetry in Time Leads to conservation of energy Symmetry in Displacement Leads to conservation of momentum General Physics C1 8 4

5 Fundamental Particles Fundamental Interactions General Physics C1 9 General Physics C1 10 5

6 Macroscopic Interactions Standard Prefixes General Physics C1 11 General Physics C1 12 6

7 Benchmarks for Distance, Time, and Mass Movie Powers of 10 General Physics C1 13 General Physics C1 14 7

8 Unit conversion examples Distance Convert 3,256 m into km Unit conversion examples (con t) Rate Convert 20m/h to km/s Convert 237 feet to m (hint: 1 foot = m) Convert 10 miles to km (hint: 1 mile = 1609 m) General Physics C1 15 General Physics C1 16 8

9 Group Problem Which speed is faster? 60 miles/hr 30 m/s Show your answer with Virtual Classroom Unit conversion examples Density - from p. 19 of the book Consider a rock with density 3000 kg/m 3 and volume 10 cm 3 What is its mass? Given:! = 3000 kg/m 3, V = 10 cm 3 Find: m! = m/v m =! x V 3 * 1m '* 1m '* 1m ' " 10cm #( %( %( % 0. kg * kg ' m $! + V $ ( 3000 $ 03 3 % ) m & ) 100cm &) 100cm &) 100cm & General Physics C1 17 General Physics C1 18 9

10 Group Problem The density of water at standard temperature and pressure, is 1g/cm 3. What is the density of water in SI units, which would be kg/m 3? Vectors and Scalars scalar quantity completely specified by a single value with an appropriate unit and has no direction. Use an italic letter: A vector quantity completely described by a number and appropriate units plus a direction. Use an arrow: A General Physics C1 19 General Physics C

11 Pig Activity Determine position of pig in three dimensions (x, y, z). We ve described the position by three scalar values. A vector has both magnitude (number value) and direction.! p $ Show magnitude or value p xˆ, p yˆ, x p zˆ General Physics C1 21 y z Show direction Column Vector How can we describe this position using a using column vector?! p $ p xˆ, p yˆ, p zˆ x 2 p p! $ 0 0 p 01 p x y z / y General Physics C1 22 z typical vector notation column vector notation Write your pig position in typical vector notation column vector notation. 11

12 Magnitude and Direction Direction A vector may also be represented by it s magnitude and direction. Magnitude! p $ mag, " p# $ p, p p The magnitude of the vector has physical units The magnitude of a vector is always a positive number x y z Based on forming a right triangle from r and 3 x = r cos 3 y = r sin 3 SOH-CAH-TOA H O Find the magnitude of your pig vector. A General Physics C1 23 General Physics C

13 Cartesian to Polar Coordinates r is the hypotenuse and 3 an angle 3 must be counterclockwise from positive x axis for these equations to be valid Think-Pair-Share Jane leaves her house and walks 5.0 blocks east and then proceeds north until she is 7.8 blocks from home at an angle of 50 degrees North of east. How many blocks north did she travel? General Physics C1 25 General Physics C

14 Direction of pig Determine the direction of the pig. y tan3 $ x 41* y ' 3 $ tan ( % ) x & General Physics C

Coordinate Systems. Chapter 3. Cartesian Coordinate System. Polar Coordinate System

Coordinate Systems. Chapter 3. Cartesian Coordinate System. Polar Coordinate System Chapter 3 Vectors Coordinate Systems Used to describe the position of a point in space Coordinate system consists of a fixed reference point called the origin specific axes with scales and labels instructions